Related papers: A weighted minimum gradient problem with complete …
This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…
In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model, we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity…
Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…
This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
We consider the Bean's critical state model for anisotropic superconductors. A variational problem solved by the quasi--static evolution of the internal magnetic field is obtained as the $\Gamma$-limit of functionals arising from the…
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force.…
This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of…
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…
This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…
The idea of replacing an edgy perfectly conducting boundary by the corresponding interface filled with a dielectric material of extreme complex permittivities, is examined in the present work. A semi-analytical solution to the corresponding…
We present transport measurements of electrons on the surface of liquid helium in a microchannel device in which a constriction may be formed by a split-gate electrode. The surface electron current passing through the microchannel first…
In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…
We deal with the problem of determining the shape of an inclusion embedded in a homogenous background medium. The multifre-quency electrical impedance tomography is used to image the inclusion. For different frequencies, a current is…
We revisit the question of existence and regularity of minimizers to weighted least gradient problems on a fixed bounded domain, subject to a Dirichlet boundary condition, in the case where the boundary data is continuous and the weight…
We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is…
We consider the minimization problem of an anisotropic energy in classes of $d$-rectifiable varifolds in $\mathbb R^n$, closed under Lipschitz deformations and encoding a suitable notion of boundary. We prove that any minimizing sequence…
We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are…
The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…